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Isoperimetric Regions in Nonpositively Curved Manifolds

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arxiv 1604.02768 v1 pith:AIVRSA36 submitted 2016-04-11 math.DG

Joel Hass This is my paper · ORCID
classification math.DG
keywords regionsisoperimetricballscurvedmanifoldsnonpositivelyboundariesconnected
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Isoperimetric regions minimize the size of their boundaries among all regions with the same volume. In Euclidean and Hyperbolic space, isoperimetric regions are round balls. We show that isoperimetric regions in two and three-dimensional nonpositively curved manifolds are not necessarily balls, and need not even be connected.

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  1. Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds

    math.DG 2019-08 accept novelty 7.0 of 10

    The paper proves in all dimensions that the total curvature inequality implies the isoperimetric inequality in Cartan-Hadamard manifolds, and establishes a new comparison formula for total curvature of level sets.

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